Graphical display of kruskal\u27s algorithm in 3d space

V diplomskem delu smo implementirali aplikacijo za demonstracijo Kruskalovega algoritma nad oblaki točk LiDAR v 3D prostoru ter izmerili čas algoritma in čas upodabljanja, kakor tudi pomnilniško zahtevnost algoritma. Poleg tega smo tudi primerjali uporabo evklidske razdalje in intenzitete kot cene povezav. Zato smo ustvarili namizno aplikacijo, ki prebere točke LiDAR in jih izriše v 3D prostoru. Nato izvede Kruskalov algoritem nad temi točkami ter prikaže vmesne rezultate algoritma. Zaradi velikega števila začetnih povezav grafa smo uvedli aproksimacijo s pomočjo enakomerne mreže. Ugotovili smo da je uporaba intenzitete kot cene hitrejša od uporabe evklidske razdalje. Ugotovili smo tudi, da poraba pomnilnika narašča linearno glede na število vozlišč. Poleg tega smo preučili, kako nam gradnja minimalnega vpetega drevesa omogoča lažje preučevanje točk.In this thesis, we implemented an application for the demonstration of Kruskal\u27s algorithm in 3D space on LiDAR point cloud, and measured the time of the algorithm and the time of rendering, as well as the space complexity of the algorithm. In addition, we also compared the use of Euclidean distance and point intensity as the cost of edges.Therefore, we created a desktop application that reads the LiDAR point cloud and presents it in a 3D space. Then the application runs Kruskal’s algorithm over these points, as well as displays the partial results of the algorithm. Due to the large number of initial connections of the graph, we introduced an approximation using a uniform grid. It can be seen that using intensity as cost is faster than using Euclidean distance. We also found that memory consumption increases linearly with the number of nodes. Additionally, we examined how building a minimum spanning tree allows us to examine points more easily